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ABSTRACT

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Barnett, George A.On the Nature of Synonyms: end This LittiePiggie....Kay 793(4 p. ; Paper present ed at the Annual Meeting ofEastern Communication Associa ti on (Philadelphia,Pennsylvania, may 5-7, 1979)

MF 01/PCO2 Plus Postage...Behavior Theories; Higher education; LanguageAttitudes; language Pesea roil; *Lang cage Usage ;Language Variat ion: linguistic Theory;Multidimensional Scaling; *Semantics; *WordFrequency*s ynon yens

An experiment was conducted to investge.te the natureoaf synonyms by using multidimensional scaling. The selected conceptw as pig" and three of its synonyms--11hcg," "boar," and "swine."ir he se terms vary in their frequency of use in English, which makespossible to explore a behaviorally based theory of meaning. Subjects

ere -randomly assigned to one of four conditions where they p erformpedirec t pair comparisons with one of the four "pig" terms, a series of

barnyard d animal names, att.ributes, and a concept of self. The meansc f ese four groups were entered into a multidimensional analysis.En contra st to the logical assumption that synonymous words wouldproduce identical multidimesional spaces, the re sults, in fact,sugge st that the four "pig" terms are not rea3.1y equivalent, varyingsystematically in their meanings, in their use, and in their relationo positive attributes. The systematic variance in their meanings is

such that each concept Is distancte from self on the multidimensionals cale is inversely related to the frequency at which the concept: isused in English. This further suggests t hat mea.ning is behaviorallygoverned, and that any symbol's meaning is a r empirical question`hose answer de pen -is on me asurino tha actual users of that symbol.( kith or in)

*A * *

Re*** * * ** ** ***** ********ductions supplied by EDRS are the best that can be made

from t he original document.************** ***************** *****

* * *

U S 0 EP AN TPA( T OF ME ALTII.EDUCATION .WELFARENTIONAI, INSTITUTE OF

EDUCATION

TH.; DOCUMENT HAS BEEP/ REC.I70-01/CED EXACTLY AS N EC tivc .c NOMTHE PERSON ON ONCAka&TION ON 'GIN-ATINO if POINTS OF VIEW Co opiNioNsstA TED 0.0 NO rreccs94AILT REPRE-5EP4 T OFF ICIAL NA IIONAL INSTITUTE OFEOLICA TION POSIT ION OF FOLIC

'PERMISSION TO REPRODUCE THISMATERIAL RAE BEEN GRANTED BY

George A. Barnett

TO THE EDUCATIONAL RESCUEINFORMATION CEN TER (ERIC!

ON THE NATURE OF SYNON TBIs LITTLE FIGGIE.

George A. BarnettCommunication Research Laboratory

Department of Language, Literature,Communication

Rens laex Polytechnic InstituteTxoy, N.Y. 12181

Presented to the Eastern Co nunication Association, Philadelphia,

Nay 4-7, 1979.

The author would like to thank David R. Brandt, Janes W. Dinkelacker,Joseph Woelfel, Tracy Tuffillaro, Michael Thompson and Robert Oldendorfwithout whom this paper would not have been possible.

ON TE-IE N Tri RE OF va THIS LITTZ E

ABST \CT

This paper investigates the nature 'c synonyms through tbe- use of

multidimensional scaling ( IDS). While ening of any word may be defined.

by pattern of relationship or dissimOarit om all other lexical items,

a theoretical problem arises with syn try . Be a- the discrepancy of any

concept and self is zero, it logically follows that if two symb ols

synonyms that their discrepancy should also be zero. But a symbol's meaning

is dependent on. host the word is used. Thus, while two words may refer to the

e referent they may be used differently and therefore have different meanings.

An experiment was conducted to investigate the nature of synonyms. The

selected concept was PIG and three of its .synonyms, HOG, BOAR and SWINE. These

tez,Ls vary- in their frequency of use in English which made it possible to -cpIore

a beh iorally based theory of meaning. Subjects were randomly assigned to one

conditions where they performed direct pair comparisons with one of the

"pig" terms, a series of ba nyard animal names, attributes and a concept of self.

The means of :here four groups were entered into a multidimensional analysis.

the four words were in fact synonyms, then the resulting multidimensional

spaces ld be identical.

The results suggest that these four terms are in fact not equivalent.

Their meanings vary systematically. The concept's distance from self is

inversely related to the frequency at which that concept is used in English.

The results are than discussed in terms of a behaviorally based theory of meaning

and finally suggestions are made for future research.

ON THE .NAB tl OF S AND THIS L TTLE PIGGIE....

TI-MORY

The lo- a1. thecry behind the use of metric multi _ensional scaling for

the measurement of meaning and linguisti

,where (Be-

s -he been described else-

1976; Woelfel, 1977). Rather than attempt a ly detailed

discussion here, an adumbration of the theory will he furnished which should

sufficieil_ly acquaint the reader with the theoretic foundations of this research.

The meaning of any word. may be defined by its pattern of relationship or

degree of dissimilarity from all other lexical ites. Thus, the definition

of a word may be represented by a 1 X N vector,1 I.'.r in, where Sik

dissimilarity of concept 1 and k; and the

ing of any set of words by a N X N matri where any entry Sid represents

the distance between concepts i and j. Typically, S i=s averaged among a repre-

sentative sample of users of a language to take into account the consensual

nature of that code system (Woelfel, 1975;Bai e 1975).

represented in the dist

s matrix has certain mathematical properties which it amenable

to multidimensional scaling. It is a sure symmetrical matrix, whose diagonal

elements are zero (The dissimilarity of concept and itself equals zero by

definition.) and off diagonal elements may be any positive real number. This

final property makes the precise measeent of meaning possible.

A theoretical problem arises when dealing with synonyms, ire.., words with

equivalent meal ing.I

Because the discrepancy of any concept and itself is zero,

it logically follows that if two symbols are synonyms, they refer to the iden-

tical referent, that their discrepancy should also be zero (Ogden & Richards,

1946). In teens of word-substitution, if two words are semantically identical,

then the Ia can repl-

relat nsip among t)-Je symbo

former without alteration in the inter-

nix S) . If they are of synonyms, the

words are sem- ti different, then the first symbol not be replaced

by the second 'thoz.t. eitering the structure of the relations (Osgood et

1957). The greater the dissimilarity between the terms, the greater the

interrelationship among, the terms will be alte

Thus, it is expected that differences among semantic structures generated

withwith. ynanyms should be zero. That is, Si should be equivalent to Si where,

mi is the semantic structured generated with concept i, and 54, the

semantic structure generated with c pt j. Concepts i and j are considered

to be synonyms. This suggests hypothesis one:

H1.

The semantic Sistructures, S and will besignificantly different.

Hypothesis one is couched in terms such that the null hypothesis of no dif-

ference is expected. However, in which will allow for falsification, the

theoretical hypothesis is expscted to be rejected in favor of the null.

ittgenstein U953) has pointed out, meaning is dependent on how a word is

used. Also, empirical investigations using MDS have shown that one's behavior

effects the structure of scaled concepts, such that the more frequently one

performs a behavior the closer that concept is to a concept of self. (Barnett

et al., 1974; 1976; M ier 1975; Barnett & McPhail, 1979)- Linguistically,

this suggests that the more frequently use_ f a 1- guage speak or write a

word the closer that lexical iten will be to a concept of self. Additional-1Y,

synonomous symbols may be used select= vely with different domains such that

one word is used in one semantic domain acid its synonym exclusively in another'

they refer to the same referent. Thus, while two words may be considered

synonyms, i.e., refering to the same referent, they may in fact have different

ngs and a different semantic structure depending on their use.

This discussion suggests the second hypothesis:

142: The semantic structures generated by synonyms will besystematically distorted from equivalence such thatthe synonym that is used more frequently will be sig-nificantly closer to a concept of self than its synonymwhich is used less frequently.

In order to empirically assess the preceding hypotheses, the following

study was conducted.

THODS

The semantic structure of an individual may be measureu through the use

of metric multidimensional scaling--M.D.S. (Barnett, 1976). The method takes

f dissimilarities (or distances) such as matrix S and converts the

data to a series of loadings on a limited. number of dimensions. Mathematically,

the process is analogous to converting a matrix of city to city mileages to a

graphic representation such as a map. In that special case an N x N matrix of

ies (N= the number of cities) would be reduced to a two dimensional configu-

ration with little loss of information.

Barnett (1972) and Danes and Woelfel (1975) report reliability coefficients

the method of .85-.90 with as few as 50 cases and discuss w of increasing

the overt_ e reliability by the number of selection of concepts. Gordon (1976)

reports reliabilit es ranging from .933 to .988 with approximately 100 subjects

in 9 differ -nt conditions. The predictive validity Hof time se es metric M.D.S.

has been demonstrated by Marlier (1974) in a test of social judgment theory,

and by Barnett, et al., (1976) who demonstrated that the outcome of . political

campaign could be accurately predicted with this method.

M.D.S. has been used extensively to study human information processing

(Schroder, et al., 1967; Rips, et al., 1973; Runnelhart & Abrahamson, 1973) and

to measure semantic structure (Miller, 1969; Henley, 1969; Szalzy & Bryson,

1974, Barnett, 1977a, 1977b) .

Hypotheses Operationelized

Theoretical hypothesis one may be operationalized'as follows:

The multidimensional spacessignificantly different.

and will be

may be tested in the following manner. Generate two or pore multidimensional

spaces from a series of identical concepts with the exception of a single

concept--the synonym. It would vary across conditions (Si and Sj). Next,

through a series of translations a=nd rotations, minimize the degree of departure

from congruence among the spaces. Then, through the use of -tests, using the

concepts: as the unit of analysis, determine if the differ ces among the spaces

differ significantly from zero.2 When a number of spaces need to be compared,

a more parsimonious solution is necessary. A more elegant way to test for

significance would be to use the spaces as the unit of analysis. Once each

space has been rotated to congruence with each other space, there are N(N-1)

values. They are expected to be zero. Then the test for significance will be

if the mean this set of values differ significantly from zero.

The multidimensional spaces generated by synonymswill be systematically distorted from equivalence(congruence) such that the synonym that is used morefrequently will be significantly closer to a conceptof self than its synonym which is used less frequently.

Hypothesis two ay be tested as follows. One criterion for the selection

of synonyms to be scaled should be their variance in frequency of occurrence

in English. This may be determined by consulting any of the standard references

on word frequency (Tho r--dike & Large, 1944; Carroll et al.r 1971) . Additionally,

some concept of self, such as or "myself" should be scaled. Then use the

-5-

mean pair-wise distance estimate between each of the srnonyrn and the self-

concept and the variance of the individual estimates to test for significant

differences in the predicted direction. The symbol which is used in greater

frequency should be closer to self concept. A simple t-test may be used

to test for significance b t een individual condit=ions. However, to test

overall order among a nurser of conditions for significance linear trend

analysis (Hays, 1973: 691-694) stould be used. Linear trend analysis

operates in the same manner= as any comparison among means. However, since

analysis of variance in the linear case agrees exactly with linear regression,

the latter method may be used. The significance test will be performed on

the correlation between the predicted rank order and the distances between

the synonyms and the self. This test may also be performed with the actual

frequencies of occurance and the distance estimates.

In e tation

The instrument used to test the above hypotheses was composed of 66

direct pair - comparisons based on 12 different concepts. using the criterion

standard (metric) of red and white as 50 "galileos" apart. The questions were

asked in the following form: "If red and white are 50 galileos apart, how

far apart are sheep and goats?" This process was repeated for all 66 pairs.

In th is --erp a 12 by 12 dissimilarity matrix was generated. This matrix

was then be averaged across dividuals producing a mean distance matrix

which would next be converted into a multidimensio a1 space to examine the

meat he words presented below. The scaled concepts were:

1. Bad 5. Hog 9. Sheep

2. Myself 6. Horse 10. Attractive

3. Cow 7. Cat 11. Goat

4. Beneficial B. Good 12. Pig- Hog - Hoar -Swine

These conceots were chosen -f reasons. First, was the

selection of a symbol which has a variety of synonyms that sufficiently

varied ire their frequency of oecur ence in English. The concept "pig"

its eauivalents, "hog", 'boar " wine" met this criterion. According to

Thorndike 4 L _g (1944), "pig" occures 44 times per million words, "hog"

14 times, "boar" it and '

As evidence these terms are infect synonyms their definitions a -

cording to Webster's New In Dnal Diction are presented below.

Note that each definition makes reference to at least one other of the words.

boar--the uricastrated male of swine, the wild hog

hog--a domestic swine, a pig, sov or boar

pig--a young swine of either sex that has not reached sexual maturity,

a swine of any age, domestic or wild

swine--any hooved mammal of the hog kind, a hog

Additionally, the words are often used interchangeably, In a recent

article on pigs in National Geographic, the author used all four words

equivalently to refer to the same referent. Their frequency of occ _e

in the art-le were: "p ' 104; " ' 22; "swine", 11; and "bear",

(Britt, 19,8).

Second, the domain of animal names (cow, dog, horse, cat, sheep and goat)

was chosen because theoretically valid results have been obtained by scaling

such lexical items (Henley, 1969). Additionally, as Woelfel et al., (1978)

and Woelfel and Fink (in press) have shown, the meaning of a word is dependent

on the domain in which it is scaled. The " " concept could have been scaled

in a different domain, say political terms, producing an entirely different

solution. Further, one may argue that the frequencies reported by Thorndike

and Lorge were primarily generated while those terms were used in the animal

9

-7-

domain rather than in some other context. Thus, the frecueneies of occurrence

estimates may have less predictive power if the synonyms were to be scaled in

some other domain

Third, a number of attributes (bad, beneficial,' good and attractive)

were also scaled to define the synonym. Cody (1976) has shown that the scab

ing of objects elative to evaluative adjectives provides theoretically

important results in terms of implicit personality theory. Finally, the

scaling of these concepts along with a concept of self, "myself" makes it

possible to test hypothesis two.

The twelve individual concepts were placed in random order and then

the pairs were ordered as specified by the Ross Matrix (Ross, 1939 ). The

Ross Matrix optimizes the order for stimuli in the method of pair comparison.

The method maximizes the distance between a stimulus and itself in the order

of presentation and equalizes the number of times stimulus appears as the

first or second member of the pair. In this way, the effects of order can

be minimized.

and Subjects

Four alternative instruments were developed. They varied only

terms of which synonym was presented to the subjects. In every instance where

the word "pig" was presented in one condition it was changed in the different

conditions to "hog", "swine", or "boar". Subjects were randomly assigned to

one of the four conditions. The questionnaire was administered in the spring

of 1978 to classes of undergraduates at an eastern technological uftiver ity.

Administration took 30 minutes. The sample sizes for each condition were:

"pig", 44; "hog", 51; "boar", 47; and "swi=ne ", 51.

10

RESULTS

The mean distance ma

-8-

ces for the four groups are presented in tables

one through four. These matrices were transformed to spatial coordinates

using DOS (Torgerson, 1958). The first three real dimensions of the spatial

coordinates for all four groups combined axe presented in figure one. These

three dimensions explain 88.5% of the total (real & imaginary) variance in the

overall coordinate system.- The displayed locus for the individual synonym

was generated as follows. For each condition a set f spatial coordinaras

was produced. Then, each of the four spaces were rotated to congruence with

the overall space using only the unmanipulated concepts. The synonym was

allowed to vary, yielding the coordinate values plotted in figure one. This

analytical proceedure is explained below in greater depth.

[TABLES ONE TO FOUR AND FIGURE ONE ABOUT HERE]

In order to compare the four groups, the spatial m nifolds were rotated

to a 1- st square best fit congruence using all n-1 (Li) dimensions (Woelfel,

et al., 1975). The mean difference among the four gimps was 40.83 units,

indicating substantial differences among the groups. This suggests that

semantic structures generated with concepts considered to be synonyms are

not equiv alent.

In order to determine the variance among the groups could be system-

atically attributed to the synonym rather than the variance of the other concepts,

the spaces were again rotated to congruence. This time only the theoretically

staple concepts were included. That is, this rotation attempted to minimize

the discrep es among the concepts which were a anipulated in the design.

The "pig" concept was allowed to vary. It was not included the rotation.

The algorithm necessary to perforjn this analysis is described by Woelfel, et

al., (1975). A computer program which performs the necessary operations is

known as Galileo IV is available at a

(Woelfel, et al., 1976a).

f academic institutions

The results of these rotations are revealing. The average root mean

square among the groups including the synonym was 33.95.4 The mean calculated

without the "pig" concept was only 27.59, or only 81% as large. This indicates

that 19% of the overall difference among the groups can be attributed to the

difference in meaning among the synonyms. The average mean difference among

the four synonyms alone was 54.94 or almost twice (1.99 times) as large as

the difference among the groups attributable to the unrnanipulated concepts.

Worth noting are the standard deviations around the various means reported

above. The standard deviation of the differences among the groups with the

synonyms included was 10.81. Without the synonyms, it was only 4.11. This

coefficient for the differences among the synonyms was 22.23. Clearly, as

expected, the semantic structure is quite stable across the four groups when

the experimental manipulation was not included in the analysis. With the

synonym included, it is considerably larger, indicating that the manipulation

is the major source of the instability among the groups. The differences

among the groups are summarized in tables five to eight.

[TABLES FIVE TO EIGHT ABOUT HERE]

In terms of hypothesis one, all four spaces are significantly different.

Thus, the expected null hypothesis of no difference among the semantic spaces

can be rejected in favor of the theoretical hypothesis. The overall t for the

ordinary least square rotation (X = 40.83) was 101.79 (1).001). For the root

an square rotation including the synonym in the calculation of the mean but

not in the rotation (i = 33.95) t = 10.41(p.001). And the value for the

above rotation without the synonym. in the calculation of the mean (X 27 .59)

was t = 22.27 (p.001).

Since there are significant ddff<er nc

to the synonym, it is worth exarindng- how they Cif

the mechc

e four groups a tribut

icier to determi

by ,which people orgamize their semantic fractures. Tie

apparent way in which the synonyms ' loei differ is with respect to tie self.

As predicted, the concept "pig" is closest to trie concert myself, 133.58 units ;

"hog" is next, 150.37 units; with "boar" and " the same distance fiom

the self, 171.00 and 174.38 units zepectively.

Similarly, the two positive attributes scaled_ in the space, beneficial

and attractive, show a similar pattern.. With both, "pig" is the closest to

attribute, followed by "hog" , "boas" "swLne". The di t s for beneficial

139.77 attractive, thiose

distances are 108.26, 157.81, 168. 5 and 197..26 units. Wl it there are other

are respectively, 74.29, 92.81, 10

differences among the groups , they do not appea e systenut. - The reader

is invited to examine tables one tc four in order to dis other syserriatic

differences.

In tems of hypothesis two, tie linear t=rend analysia slowed that the null

hypothesis can be rejected. The amalysis was performed with both the rare

order of the frequency of occurrence (times per million words) and the actual

frequency of occurrence in English . The F-vaines were 31. 33 and 18. 00 respec-

tively. Since direction was sped. fi d, the F-v_ 1 e necessary to reject tie

null at the .05 level with degrees of fxeedom 1, 2 (1 sras 9 -26. 4

In the case of the positive attributes tiotri are significantly relate

distance from the self. The trend ar,.al +sis revealed a r 33-33 for beneficial

(1).< .05) and F = 13.29 (p<.05) for attractive :

suuma.ry, both hyp these s f ppOrt from tine data. the seanti c

spaces are significantly different and the difference can in part be accounted

by the changes in. tfie distance from the self for the synonyms. The more

frequently the lexica -1 Atern is lased it English , the closer trxe symbol is to

a concert of self. Unenect dl i_lar results were found with a pair of

positive've tt ibute s, beref i.cial ana attractive The' may also contr-ibute to

the difference aniting the semantic Etr ctures. The i_rnplicati ns of these

findings rill be discussed below.

DISCUSBIO

The results of the above araalysi suggest that the semantic stuot.

individually generat d -romp a set of synonyms are not equivalent. Despite tale

fact that the syno~nyrns refer to the same referent, tlese str,rctur'es have

systematic differences in meaning xehOered by the individual symbol s unique

relation to other lexical items used to define that sy L. These -variations

seem to be beha-viorally based, such that the more frequently a word is used,

the closer that concept will be to a concept of self . 'Thus, the results lend

support for a consensual behavio raJ1y based theory of meaning (Barnett, 1976 ).

Of special note is the serendipitious finding that the more fr quanta), a word

is used, the closer that symbol will Ice to positive attributes used to define

it. This result is con. isteilt witt tbie results discussed by Zajonc (1968).

Mere_ exioosure to a stimulus will produce a positive evaluation of that stimmlus.

Further , the more people are exposed to a stimulus, the more they will like it,

Indeed, as Zajonc pointed out, for 154 antonym pairs chosen from T'hcrndike arid

Large, 82% of the positive _ymbols occur more frequently and they awe preferred

by a majority cf a Sample of college students . This further suggests that mean-

ing is Iehaviorally governed and tilat the meaning of any symbol is an empirical

ques-tiori. It cannot be determined by a small group of vise risen composing lexica-

graphies, but oust be determined by measuring the actual users of that symnbol.

-12-

One obvious implication of the obtained results is that the researcher

should take special care in the selection of concepts when using MDS.

'These concepts should come directly from the same users of the symbols

that will be asked to perform the pair-comparisons. This is especially

true if the reason for the research is to alter a population-s attitude

toward a given object. It has become standard practice in "Galileo" rese

to perform a series of open-ended interviews to generate the actual concepts

people use to evaluate a political campaign or commercial product. The

unacceptable alternative is for the researcher to impose a set of concepts

on subjects to use when evaluating an object. This may result in a m s-

leading solution and an unsuccessful message campaign, even if the choice of

the symbols is only among a set of synonyms. For example, Woelfel et al.,

(1976b) identify a set of mathematical procedures to identify optimal message

strategies from the loci of stimuli in the spatial manifold. These procedures

were carried out on the four different groups in the study in order to

determine the optimal persuasive message so that the "pig" term would be

redefined closer to the self. Only 57.4% of the messages which would shorten

the distance between these terms were common to all four groups. In this

case, the differences between the conditions were only synonyms. Thus,

special attention should be paid to the selection of stimuli for MS.

There are a number of weaknesses in this research which should be pointed

out. The most serious of these is the use of Thorndike and forge to estimate

the synonyms' frequency of use in English. Published in 1944, the word

were based on documents published prior to that date. Thus, the frequency

estimates are at least 35 years out of date. Language changes over time and

thus those estimates may lead to erroneous conclusions. In addition, the use

of this method does not provide a measure of the frequency at which the actual

-13-

subjects use these terms. An. alternative procedure would be to have subjects

provide subjective estimates of their use of the words and use these measures

to predict semantic structure.

Another methodological shortcoming is the exclusion of the word "sow"

an additional condition. A " is "an adult female swine, a female hog of

any age." This lexical item occurs less than one time per million words. Its

inclusion would increase the variance in the frequency variable and this

increases the confidence in the stated conclusions.

This condition becomes asingly important when gender is considered.

One of the additional attributes which differentiate these synonyms is sex.

"Boar" represents the male of the species. "Sow" the female. "Pig", "h g",

n-" do not make reference to gender. This suggests that "male" female"

should have been added to the concept list. Also, "wild" and "domestic"

should have been included. The synonyms could also be differentiated by this

pair of adjectives.

The results reported here suggest some future research. This report is

only part of an ongoing study to test serum of the theoretical ideas of Woelfel

and Saltiel (1975). They suggest the attitude change is inversely related to

the

the

al mass of the concept being altered. Inertial mass nay be taken to

ation history of the concept. Frequency of occurrence may provide

a reasonable estimate of a concept's mass. Thus, it is expected that if the

same persuasive message were presented to the sane four groups and then a post-

test measure made that "pig" would be the most stable, then, "bog", "boar",

with "swine" having the greatest attitude change. The second half of this study

is planned to test these ideas. With the results from the message generation

procedures (W lfel et al., 1976) a persuasive message has been written.

says that rigs ", thogs, boars, s

-14-

(sow] -ebeneficial" and "attractive".

This message maximized the predicted motion toward the target concept, " y-

self", for each of the individual groups and the four groups combined. A

separate group post-test design will take place and the results compared

with the ones reported here and the appropriate contrc groups. In this

way, it will be possible to determine the utility of frequency of occurrence

in English as an indicator of inertial mass and further insights into the Woelfel-

Saltiel theory may be gained. Finally, a fifth condition, "sow ", will be

included in the post -test along with the subjects' subjective estimates of

their frequency of use of these five synonyms.

In summary, this paper has investigated the nature of synonyms and found

that they are not equivalent in meaning (septic structure) despite referring

to the same referent. Systematic distortion from equivalence occurs due to

variance in the use of the te- d in their relation to positive attributes.

These results were next discussed in terms of a behaviorally based theory of

meaning. Finally, future research ideas based on the reported findings have

been discussed.

17

NOTES

1. This paper assumes a strict definition of synonym, i.e., words whichexpress identical or equivalent meaning and may be equally well interchanged.They may be defined wholly, or almost wholly, in the same terms. Historically,there has been considerable debate over the definition of the term synonym.For a complete historical review and statement of the current status on theissue of synonyms see the introduction of NewPhilip B. Grove, .editor (1973).

2. The use of significance tests and, inferential statistics of any sort runsagainst the spirit of metric MDS. Metric MIS is a series of continuous ratioscaled distance estimates. It assumes the height of absurdity to reduce theseestimates to a dichotomous decision of an acceptance or rejection of the nullhypothesis. These data can and should be used as a description of the semanticstructure of individuals or groups. Thus, one could say they describe acertain relationship without attempting to infer beyond the sample of subjectsor concepts. Additionally, these data axe based on a large number of indepen-dent observations of the relationship between a particular pair of concepts.This notion is not taken into account by this significance test, where theunit of analysis is the number of concepts or spaces and thus the degrees offreedom are some small numbers rather than the number of independent observations.

3. Imaginary variance results because the multidimensional spaces are non-Euclidean. That is, the mean distance matrices are non-positive semi-defini e.This problem is explained further in note three and by Woelfel et al. (1978)

4. Root mean squares were calculated rather than ordinary means because someof the difference between the groups could be attributable to differences onthe imaginary dimensions. The imaginary dimensions result because the semanticstructures are non-Euclidean. In this case, the mean proportion of varianceon the imaginary dimensions was 25.8. Non-Euclideanisms result in semanticspace because the meanings are incongruent and great distances in space betweensemantic domains are not adequately described by a linear metric. For a morecomplete discussion see Woelfel, et al. (1978).

5. The individual t-tests find only one of the differences significant atthe .05 level (Pig-Swine) and one (Pig-Boar) significant at the .10 level,although all are in the predicted direction and the overall trend is significant.The individual differences and values of t for the means among the synonymsare presented in the matrix below.

Pig Hog Boar SwinePigHogBoarSwine

0,0

16.8/.6937.4/1.5940.4/1.69

0.023.6/.9820.6/.82

0.0

3/.13 0.0

TABLE ONE

4AIILE0 MANS MATRIX--SWINE

1 2 4 5 7 9 10 11 12

1 0.0

2 156.84 0.0

3 145.52 135.00 0.0

4 180.58 57.20 82.78 0.0

5 112.18 103.42 96.07 61.70 0,0

6 115,42 103.75 57.48 76.56 73,66 0

7 104.64 73.71 112.39 131.58 124,48 93.02 0.0

8 147.36 58.77 68.78 25.72 87.08 74.81 154.31 0.0

9 137.14 140.72 69.83 84.27 87.87 70.68 80.88 114.82 0.0

10 141.36 53.14 151.42 66.39 127.11 96.90 96.55 63.47 138.61 0.0

11 124.78 145.75 80.44 134.75 87.05 64.:30 145.00 147.49 57.12 137.42 0.0

12 141.66 174.38 57.30 139.76 E6,08 85.22 114.31 81.15 70.80 197.26 77.35 0.0

TABLE TWO

--GALILEO MEANS nAT X--BOAR

2 4 5 6 7 8 9 10 11 12

0.0

149.46 0.0

43.00 79.18 0.0

161.53 82.91 94.88 0.0

150.58 65.04 75.81 104.44 0.0

157.31 134.77 113.00 71.84 102.40 0.0

35.04 90.06 28.24 85.40 105 04 96.80 0.0

136.56 70.33 72.11 83.04 70.76 81.77 69,77 0.0

45.84 131.07 50.78 80.66 83.36 75.34 48,97 111.83 0.0

167.63 74.24 93.36 67.17 70.97 101.34 95,77 48.88 153.95 0.0

171.00 75.51 109.48 74.09 89.88 122.60 84.47 115.20 168.95 82.64 0.0

TABLE THREE

0A1,11E0 MEANS MATRI --HOG

2 3 4 6 7 9 10 11 12

7

8 121.53 0.0

6 81.08 67.66 0.0

9 134.65 73.36 90.10 0.0

7 110.19 76.91 99.59 81.89 0.0

7 140.13 98.39 139.35 94.95 116.44 0.0

5 49.38 98.12 31.77 80.41 94.95 119.83 0.0

2 14634 59.72 94.06 79.25 69.84 84.30 89.97 0.0

5 52.83 127.65 59.62 103.67 92.14 103.53 68.02 105.85 0.0

6 167.52 83.20 108.36 69.79 81.35 93.46 107.37 59.35 117.72 0.0

3 150.37 76.17 92.80 74.20 80.83 98.33 69.84 78.22 158.95 75.87 0.

TABLE FOUR,

--GALILEO MEANS WM--

3 4 5 6 7 8 9 10 11 12

1 0.0

2 120,34 0.0

3 112.23 111.66 0.0

4 175,34 46.02 77.18 0.0

5 132,30 129.05 99.11 83.83 0.0

6 135,81 150.17 59.07 67.07 90.72 0.0

7 91.97 132.23 142.41 94.17 79.02 120.68 0.0

8 184.81 31.48 96.30 31.47 73.69 7073 6920 0.0

9 97.15 134.10 76.43 75.27 127.95 74.27 90.04 98.50 0.0

10 167,64 38.36 113.61 69.58 76.85 89 39 62.07 64.95 85.50 0.0

11 115,70 153.25 78..72 113.97 85.54 69.73 134.02 87.60 68,44 94.70 0.0

12 114.64 133.58 54.83 74.29 94.21 93.88 114.23 82.83 87.77 109.25 60 96 0,0

RC

TABLE FIVE

SQUARE DIFFERENCE AMONG FOUR GROUP

WITH SYNONYM*

1 2 3 4

0.0 34.27 31.28 39.96

2 34.16 0.0 28.52 35.80

31.31 28.43 0.0 35.08

4 39.92 33.27 35.26 0.0

MEAN ROOT MEAN SQUARE 33.95

STANDARD DEVIATION 10.81

* Rotation did not include synonym

S U

TABLE SU

DIFFERENCE AMOUNG FOUR GROUPS

1

WITHOUT SYNONYM

2 3 4

1 0.0 28.42 30.69 35.48

2 28.57 0.0 25.52 23.78

3 30.74 25.45 0.0 28.47

4 18.54 25.17 30.27 0.0

MEAN ROOT MEAN SQUARE 27.58

STANDARD DEVIATION 4.11

TABLE SEVEN

DIFFERENCES AMONG THE FOUR SYNONYMS

SWINE BOAR HOG PIG

SWINE 0.0 66.36 20.98 64.06

BOAR 64.85 0.0 44.16 78.62

HOG 15.85 21.22 0.0 70.97

PIG 62.75 77.84 71.63 0.0

MEAN DIFFERENCE 54.94

STANDARD DEVIATION 22.23

2ABLE EIGHT

SUMMARY OF MEAN DIFFERENCES AND 5T _DAP DEVIATIONS

LEAST SQUARE ROTATION 40.83 1.33

ROOT MEAN SQUARE WITH SYNONYM 33.95 10.81

ROOT MEAN SQUARE WITHOUT SYNONYM 27.59 4.11

FOUR SYNONYMS 54.95 22.23

FIGURE 1Three- Dimensional Space For AllFour Groups Combined With

Individual Synonyms*

=Swine14=Boar15=Hog

16 -pig

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